1. Statement of the Technical Field
The invention concerns communication systems. More particularly, the invention concerns communications systems in which phase rotation modulation encoding and decoding are performed.
2. Description of the Related Art
There are many spread spectrum communication systems known in the art. Such spread spectrum communication systems often employ modulation techniques to encode data at baseband, while spread spectrum techniques permit a system to increase bandwidths of the transmitted signals and lower the power spectral density, effectively spreading the signal energy. Such baseband modulation techniques include Frequency Shift Keying (“FSK”) modulation techniques, Phase Shift Keying (“PSK”) techniques, Pulse Amplitude Modulation (“PAM”) techniques, Phase Shift Keying Modulation (“PSK”) techniques and On Off Keying (“OOK”) techniques. Each of the listed modulation techniques are well known in the art, and therefore will not be described herein. Spread spectrum techniques generally involve combining a modulated baseband signal with a typically much higher rate numerical sequence. Such sequences can take the form of binary-level amplitude and/or phase modulations such as those used in Direct Sequence Spread Spectrum (“DSSS”) or multi-level amplitude and/or phase modulations such as those used in Chaotic Sequence Spread Spectrum (“CSSS”).
Spread spectrum signals have an added degree of freedom in the timing axis since a spread ratio “M” is determined by a data symbol rate (which defines the information throughput) and a spreading chip rate. The spread ratio “M” can be written in two equivalent ways, as shown by the following Mathematical Equations (1) and (2).M=(spreading chip rate)/(data symbol rate)  (1)M=(symbol duration)/(chip duration)  (2)Increases in the spread ratio “M” represent an increase in signal robustness and security, and a decrease in the information density (measured in bits/hertz/second). The information density is often used as a measure of channel efficiency. In effect, the higher the spread ratio “M”, the greater the expansion in signal bandwidth.
Spread spectrum communication systems typically also qualify as Multiple Access (MA) communication systems. In MA communication systems, the total channel capacity can be shared between multiple users simultaneously. The channel efficiency in MA communication systems is equal to the information density of a single user times the total number of users accessing the channel simultaneously. In theory, the aggregate efficiency/capacity of the users in an MA communication system is equal to that of a single user with the identical channel and the sum of the MA signal energies. In practice, implementation trade offs and coordination of communications between the users in the MA communication system (each of which practically have different channels) reduce the aggregate channel efficiency to significantly less than that of a non-shared spectrum. Moreover, there may not be enough users in the channel at one time to fully use the spectrum, which leaves channel capacity underutilized.
In Frequency Division MA (“FDMA”) communication systems, the excess channels can be assigned to users in the network. The users are thereby allowed to transmit either wider bandwidth signals or use additional carriers. The FDMA communication system works well when there are a small number of users. However, the FDMA communication system does not provide a significant improvement in the security of the waveform as compared to that of other communication systems since the instantaneous energy density of a channel in use is relatively high.
Frequency hopping FDMA communication systems (that are well coordinated by a shared time basis) improve the robustness of the transmitted signal against interferers (anti-jam characteristics). Still, the detection characteristics of the frequency hopping FDMA communication systems are not significantly improved over non-frequency hopping FDMA communication systems. In this regard, it should be noted that frequency hopping reduces that average energy density, but not the instantaneous energy density.
In Code Division MA (“CDMA”) communication systems, modulated signal energy is spread broadly over a large frequency spectrum. As a result of this spreading, the instantaneous and average energy densities are reduced. As such, the CDMA communication systems have improved robustness, anti-jam characteristics and probability of detection characteristics.
The most common spread spectrum technique employed by CDMA communication systems is a DSSS technique. Although DSSS based CDMA communication systems improved the security of transmission, they still suffer from certain drawbacks. For example, the signals generated by DSSS based CDMA communication systems have cyclo-stationary features subject to detection by feature detectors.
The advent of digital chaotic spread spectrum communication systems allows for spread spectrum transmission of signals without the presence of cyclo-stationary features. The elimination of the cyclo-stationary features limits the detection capability of an adversary to only energy detection. One of the greatest benefits of chaotic spread spectrum signals is that interfering energy received in band is averaged over the entire bandwidth. As a result, the digital chaotic spread spectrum communication systems have better overall performance as compared to other communication systems. Despite the improved performance and robustness of the digital chaotic spread spectrum communication systems, they still exhibit limitations. For example, the information rate of digital chaotic spread spectrum communication systems is limited by the range of adaptability in the spread ratio “M”. As such, an individual user's channel efficiency, when security is maximized, is often limited to an order of magnitude around one and ten hundredth (0.01-0.10) of bits per hertz per second. Lower spreading ratios tend to eliminate the traditional advantages of spread spectrum communication systems.
There is a desire to increase this channel efficiency so that a single user is allowed to increase his/her total information delivered without increasing the spreading chip rate or the data symbol rate. One method to do this is to spread data symbols that have multiple levels of baseband phase and amplitude modulation. In this scenario, the amount of data delivered is increased linearly by the base-2 logarithm of the number of points in a signaling constellation.
Another method to increase the channel efficiency is to employ a Pulse Position Modulation (“PPM”) technique. In PPM, the data of a transmitted symbol is encoded into one of a plurality of timeslots within a pre-defined frame or epoch and then detected using techniques similar to on-off keying modulations. As an example, a PPM encoding scheme conveys all of its energy in a single timeslot chosen out of a total of “W” possible timeslots, thereby permitting transmission of log2(W) bits of data each epoch. PPM techniques are well known in the art, the therefore will not be described in detail herein. However, it should be noted that the performance of a PPM based communication system is limited by the number of total timeslots since one (1) timeslot where the pulse is transmitted must overcome the random energy accumulation occurring in the other timeslots. An approximated performance in a stationary channel of the PPM based communication system is defined by a stochastic decision between W-1 independent noise accumulations and the intended (unknown) single signal plus noise accumulation. Increasing the value of W leads to greater potential for false positives, and therefore a higher required Signal-to-Noise Ratio (“SNR”). Such a process can be quantified using order statistics. Order statistics are well known in the art, and therefore are not described herein. In general, PPM is a very simple and computationally efficient modulation technique. However, other modulation techniques provide better data throughput performance for high SNRs.